½ - life The decay of a single nuclei is totally random However, with large numbers of atoms a pattern does occur

½ - life This is the time it takes half the nuclei to decay half-life (t½) Number of nuclei undecayed time

½ - life This is the time it takes half the nuclei to decay Number of nuclei undecayed time half-life (t½)

½ - life This is the time it takes half the nuclei to decay Number of nuclei undecayed A graph of the count rate against time will be the same shape time half-life (t½)

Different ½ - lives Different isotopes have different half-lives The ½-life could be a few milliseconds or 5000 million years! Number of nuclei undecayed time half-life (t½)

Example

Example A radio-isotope has an activity of 400 Bq and a half-life of 8 days. After 32 days the activity of the sample is A – 200 Bq B – 100 Bq C – 50 Bq D – 25 Bq

Example A sample contains an amount of radioactive material with a half-life of 3.5 days. After 2 weeks the fraction of the radioactive material remaining is A. 94 %. B. 25 %. C. 6 %. D. 0 %.

Example Nuclide X has a half-life of 1 day and nuclide Y has a half-life of 5 days. In a particular sample, the activities of X and Y are found to be equal. When the activity is tested again after 10 days, the activity will be A. entirely due to nuclide X. B. due equally to nuclides X and Y. C. mostly due to nuclide X. D. mostly due to nuclide Y.

Nuclear Reactions

Transmutation changing a nucleus by adding nucleons.

Fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus.

Fission either a nuclear reaction or a radioactive decay process in which the nucleus of an atom splits into smaller parts (lighter nuclei).

Unified mass unit (u) Defined as 1/12 of the mass of an atom of Carbon-12 u = 1.6605402 x 10-27 kg

Energy mass equivalence E = mc2 E = 1.6605402 x 10-27 x (2.9979 x 108)2 E = 1.4923946316 x 10-10 J Remembering 1 eV = 1.602177 x 10-19 J 1 u = 931.5 MeV

Mass defect For helium, the mass of the nucleus = 4.00156 u But, the mass of two protons and two neutrons = 4.0320 u!!!! Where is the missing mass?

Mass defect The missing mass (mass defect) has been stored as energy in the nucleus. It is called the binding energy of the nucleus. It can be found from E = mc2

Mass defect calculation Find the mass defect of the nucleus of gold, 196.97 - Au

Mass defect calculation The mass of this isotope is 196.97u Since it has 79 electrons its nuclear mass is 196.97u – 79x0.000549u = 196.924u

Mass defect calculation The mass of this isotope is 196.97u Since it has 79 electrons its nuclear mass is 196.97u – 79x0.000549u = 196.924u This nucleus has 79 protons and 118 neutrons, individually these have a mass of 79x1.0007276u + 118x1.008665u = 198.080u

Mass defect calculation The mass of this isotope is 196.97u Since it has 79 electrons its nuclear mass is 196.97u – 79x0.000549u = 196.924u This nucleus has 79 protons and 118 neutrons, individually these have a mass of 79x1.0007276u + 118x1.008665u = 198.080u The difference in mass (mass defect) is therefore 1.156u

Mass defect calculation The difference in mass (mass defect) is therefore 1.156u This “missing mass” is stored as energy in the nucleus (binding energy). 1u is equivalent to 931.5 MeV

Binding energy This is the work required to completely separate the nucleons of the nucleus.

Binding energy per nucleon This is the work required to completely separate the nucleons of the nucleus divided by the number of nucleons. It is a measure of how stable the nucleus is.

The binding energy curve

Example

Nuclear Fission

Uranium Uranium 235 has a large unstable nucleus.                                                                  

Capture A lone neutron hitting the nucleus can be captured by the nucleus, forming Uranium 236.

Capture A lone neutron hitting the nucleus can be captured by the nucleus, forming Uranium 236.

Fission The Uranium 236 is very unstable and splits into two smaller nuclei (this is called nuclear fission)

Free neutrons As well as the two smaller nuclei (called daughter nuclei), two neutrons are released (with lots of kinetic energy)

Fission These free neutrons can strike more uranium nuclei, causing them to split.

Chain Reaction If there is enough uranium (critical mass) a chain reaction occurs. Huge amounts of energy are released very quickly.                                                                                                                                    

Chain Reaction If there is enough uranium (critical mass) a chain reaction occurs. Huge amounts of energy are released very quickly.                                                                                                                                    

Bang! This can result in a nuclear explosion!YouTube - nuclear bomb 4

Nuclear fusion – Star power!

The binding energy curve